I have two Emacs instances running, one locally and the other as an X Window running on a server I am ssh-connected to. When I try to copy+paste text between one and the other, the instance running on the server can paste to the local one by selecting text and doing Meta+W, then doing Shift+Insert on the local Emacs buffer. But the other way doesn't work: by selecting text and doing Meta+W on the local Emacs then doing Shift+Insert on the server Emacs, I get either nothing, or the contents of the clipboard from another program (e.g. the browser).
I have the same .emacs file on both, so I am not sure what's making these behave differently. How can I make the Shift+Insert pasting work from local to server Emacs?